工程热力学第三版答案【英文】第9章.doc

9-13 The three processes of an air-standard cycle are described. The cycle is to be shown on the P-v and T-s diagrams, and the back work ratio and the thermal efficiency are to be determined.Assumptions 1 The air-standard assumptions are applicable. 2 Kinetic and potential energy changes are negligible. 3 Air is an ideal gas with constant specific heats.Properties The properties of air are given as R = 0.287 kJ/kg.K, cp = 1.005 kJ/kg.K, cv = 0.718 kJ/kgK, and k = 1.4.Analysis (a) The P-v and T-s diagrams of the cycle are shown in the figures.(b) The temperature at state 2 isDuring process 1-3, we havesT321vvP321During process 2-3, we haveThe back work ratio is thenHeat input is determined from an energy balance on the cycle during process 1-3,The net work output is(c) The thermal efficiency is then9-21An air-standard cycle executed in a piston-cylinder system is composed of three specified processes. The cycle is to be sketcehed on the P-v and T-s diagrams; the heat and work interactions and the thermal efficiency of the cycle are to be determined; and an expression for thermal efficiency as functions of compression ratio and specific heat ratio is to be obtained. Assumptions 1 The air-standard assumptions are applicable. 2 Kinetic and potential energy changes are negligible. 3 Air is an ideal gas with constant specific heats.Properties The properties of air are given as R = 0.3 kJ/kgK and cv = 0.3 kJ/kgK.Analysis (a) The P-v and T-s diagrams of the cycle are shown in the figures.(b) Noting thatsT321vvP321Process 1-2: Isentropic compression From ideal gas relation,Process 2-3: Constant pressure heat additionProcess 3-1: Constant volume heat rejection(c) Net work isThe thermal efficiency is then9-32The two isentropic processes in an Otto cycle are replaced with polytropic processes. The heat added to and rejected from this cycle, and the cycles thermal efficiency are to be determined.Assumptions 1 The air-standard assumptions are applicable. 2 Kinetic and potential energy changes are negligible. 3 Air is an ideal gas with constant specific heats.Properties The properties of air at room temperature are R = 0.287 kPam3/kgK, cp = 1.005 kJ/kgK, cv = 0.718 kJ/kgK, and k = 1.4 (Table A-2a).vvP4132Analysis The temperature at the end of the compression isAnd the temperature at the end of the expansion isThe integral of the work expression for the polytropic compression givesSimilarly, the work produced during the expansion isApplication of the first law to each of the four processes gives The head added and rejected from the cycle areThe thermal efficiency of this cycle is then9-37An ideal Otto cycle with air as the working fluid has a compression ratio of 8. The amount of heat transferred to the air during the heat addition process, the thermal efficiency, and the thermal efficiency of a Carnot cycle operating between the same temperature limits are to be determined.vvP4132qinqout2400 R540 RAssumptions 1 The air-standard assumptions are applicable. 2 Kinetic and potential energy changes are negligible. 3 Air is an ideal gas with variable specific heats.Properties The properties of air are given in Table A-17E.Analysis (a) Process 1-2: isentropic compression.Process 2-3: v = constant heat addition.(b) Process 3-4: isentropic expansion.Process 4-1: v = constant heat rejection.(c) The thermal efficiency of a Carnot cycle operating between the same temperature limits is9-40The expressions for the maximum gas temperature and pressure of an ideal Otto cycle are to be determined when the compression ratio is doubled.Assumptions 1 The air-standard assumptions are applicable. 2 Kinetic and potential energy changes are negligible. 3 Air is an ideal gas with constant specific heats.Analysis The temperature at the end of the compression varies with the compression ratio asvvP4132qoutqinsince T1 is fixed. The temperature rise during the combustion remains constant since the amount of heat addition is fixed. Then, the maximum cycle temperature is given byThe smallest gas specific volume during the cycle isWhen this is combined with the maximum temperature, the maximum pressure is given by9-47An ideal diesel cycle has a compression ratio of 20 and a cutoff ratio of 1.3. The maximum temperature of the air and the rate of heat addition are to be determined.Assumptions 1 The air-standard assumptions are applicable. 2 Kinetic and potential energy changes are negligible. 3 Air is an ideal gas with constant specific heats.Properties The properties of air at room temperature are cp = 1.005 kJ/kgK, cv = 0.718 kJ/kgK, R = 0.287 kJ/kgK, and k = 1.4 (Table A-2a).vvP4123qinqoutAnalysis We begin by using the process types to fix the temperatures of the states.Combining the first law as applied to the various processes with the process equations givesAccording to the definition of the thermal efficiency,9-59An ideal dual cycle has a compression ratio of 15 and cutoff ratio of 1.4. The net work, heat addition, and the thermal efficiency are to be determined. Assumptions 1 The air-standard assumptions are applicable. 2 Kinetic and potential energy changes are negligible. 3 Air is an ideal gas with constant specific heats.Properties The properties of air at room temperature are R = 0.3704 psiaft3/lbm.R (Table A-1E), cp = 0.240 Btu/lbmR, cv = 0.171 Btu/lbmR, and k = 1.4 (Table A-2Ea).Analysis Working around the cycle, the germane properties at the various states arevvP4123qoutxqinApplying the first law to each of the processes gives The net work of the cycle isand the net heat addition isHence, the thermal efficiency is9-61An expression for cutoff ratio of an ideal diesel cycle is to be developed.Assumptions 1 The air-standard assumptions are applicable. 2 Kinetic and potential energy changes are negligible. 3 Air is an ideal gas with constant specific heats.vvP4123qinqoutAnalysis Employing the isentropic process equations,while the ideal gas law givesWhen the first law and the closed system work integral is applied to the constant pressure heat addition, the result isWhen this is solved for cutoff ratio, the result is9-81 A simple ideal Brayton cycle with air as the working fluid has a pressure ratio of 10. The air temperature at the compressor exit, the back work ratio, and the thermal efficiency are to be determined.Assumptions 1 Steady operating conditions exist. 2 The air-standard assumptions are applicable. 3 Kinetic and potential energy changes are negligible. 4 Air is an ideal gas with variable specific heats.Properties The properties of air are given in Table A-17E.sT1243qinqout2000 R520 RAnalysis (a) Noting that process 1-2 is isentropic,(b) Process 3-4 is isentrop